# Margin of Error Calculator

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The Margin of error is the statistical way of calculating the random error in a given sample. It tells us to what extent the survey is reliable!. It is expressed in percentage.
Margin of Error formula is given by

Where P is the probability of proportion of population,

N gives the size of the population,

n is the size of the sample.

Suppose you are having the set of children in which there are 60% of them participating in sports. If the marginal error is 5% it means that there is possibility of 55% - 65% people participating in sports. Thus the marginal error tells you how accurate the results are!. The greater the marginal error, lesser will be the accuracy.

Marginal Error Calculator is a online tool that gives the marginal error of the given survey if the size of the population N, probability p and sample size n are entered in blocks provided.

## Margin of Error Steps

Here are given some steps to find the Margin of Error.

Step 1 : Read the problem and observe the given quantities

Step 2 : The Margin of error formula is given by

MOE = (1.96) $\sqrt{\frac{N - n}{N - 1}}$ $\times$ $\sqrt{p \frac{1 - p}{n}}$

Substitute the values and get the answer.

## Margin of Error Problems

Below are given some problems based on Margin of error which may be helpful for you.

### Solved Examples

Question 1: There are 50 people in a class, out of which 20 go by school bus. If the probability of proportion is 0.3, calculate the Margin of error?
Solution:

Given: Size of the population N = 50,
Size of sample n = 20,
Probability of proportion of population P = 0.3
The Marginal error is given by
MOE = (1.96) $\times$ $\sqrt{\frac{N - n}{N - 1}} \times \sqrt{p \frac{(1 - p)}{n}}$
= (1.96) $\times$ $\sqrt{\frac{50 - 20}{50 - 1}} \times \sqrt{0.3 \frac{(1 - 0.3)}{20}}$
= 1.96 $\times$ 0.78 $\times$ 0.102
= 0.1566
= 15.66%.

Question 2: A class contains 10 children, out of which 5 bring lunch box every day. If the probability of proportion is 0.1, calculate the Margin of error?
Solution:

Given: Size of the population N = 10,
Size of sample n = 5,
Probability of proportion of population P = 0.1
The Marginal error is given by
MOE = (1.96) $\times$ $\sqrt{\frac{N - n}{N - 1}} \times \sqrt{p \frac{(1 - p)}{n}}$
= (1.96) $\times$ $\sqrt{\frac{10 - 5}{10 - 1}} \times \sqrt{0.1 \frac{(1 - 0.1)}{10}}$
= 1.96 $\times$ 0.74 $\times$ 0.13
= 0.1945
= 19.45%.